arXiv subjects

Hyun Jong Kim

Publications and source records attributed to Hyun Jong Kim.

4 recordsLinked to original sources

arXiv2026

QEDBENCH: Quantifying the Alignment Gap in Automated Evaluation of University-Level Mathematical Proofs

As Large Language Models (LLMs) saturate elementary benchmarks, the research frontier has shifted from generation to the reliability of automated evaluation. We demonstrate that standard "LLM-as-a-Judge" protocols suffer from a systematic Alignment Gap when applied to upper-undergraduate to early graduate level mathematics. To quantify this, we introduce QEDBench, the first large-scale dual-rubric alignment benchmark to systematically measure alignment with human experts on university-level math proofs by contrasting course-specific rubrics against expert common knowledge criteria. By deploying a dual-evaluation matrix (7 judges x 5 solvers) against 1,000+ hours of human evaluation, we reveal that certain frontier evaluators like Claude Opus 4.5, DeepSeek-V3, Qwen 2.5 Max, and Llama 4 Maverick exhibit significant positive bias (up to +0.18, +0.20, +0.30, +0.36 mean score inflation, respectively). Furthermore, we uncover a critical reasoning gap in the discrete domain: while Gemini 3.0 Pro achieves state-of-the-art performance (0.91 average human evaluation score), other reasoning models like GPT-5 Pro and Claude Sonnet 4.5 see their performance significantly degrade in discrete domains. Specifically, their average human evaluation scores drop to 0.72 and 0.63 in Discrete Math, and to 0.74 and 0.50 in Graph Theory. In addition to these research results, we also release QEDBench as a public benchmark for evaluating and improving AI judges. Our benchmark is publicly published at https://github.com/qqliu/Yale-QEDBench.

cs.LG↗

arXiv2024

Global $\mathbb{A}^1$ degrees of covering maps between modular curves

Given a projective smooth curve $X$ over any field $k$, we discuss two notions of global $\mathbb{A}^1$ degree of a finite morphism of smooth curves $f: X \to \mathbb{P}^1_k$ satisfying certain conditions. One originates from computing the Euler number of the pullback of the line bundle $\mathscr{O}_{\mathbb{P}^1}(1)$ as a generalization of Kass and Wickelgren's construction of Euler numbers. The other originates from the construction of global $\mathbb{A}^1$ degree of morphisms of projective curves by Kass, Levine, Solomon, and Wickelgren as a generalization of Morel's construction of $\mathbb{A}^1$-Brouwer degree of a morphism $f: \mathbb{P}^1_k \to \mathbb{P}^1_k$. We prove that under certain conditions on $N$, both notions of global $\mathbb{A}^1$ degrees of covering maps between modular curves $X_0(N) \to X(1)$, $X_1(N) \to X(1)$, and $X(N) \to X(1)$ agree to be equal to sums of hyperbolic elements $\langle 1 \rangle + \langle -1 \rangle$ in the Grothendieck-Witt ring $\mathrm{GW}(k)$ for any field $k$ whose characteristic is coprime to $N$ and the pullback of $\mathscr{O}_{\mathbb{P}^1}(1)$ is relatively oriented.

math.AG↗

arXiv2023

Computing nonsurjective primes associated to Galois representations of genus $2$ curves

For a genus $2$ curve $C$ over $\mathbb{Q}$ whose Jacobian $A$ admits only trivial geometric endomorphisms, Serre's open image theorem for abelian surfaces asserts that there are only finitely many primes $\ell$ for which the Galois action on $\ell$-torsion points of $A$ is not maximal. Building on work of Dieulefait, we give a practical algorithm to compute this finite set. The key inputs are Mitchell's classification of maximal subgroups of $\mathrm{PSp_4}(\mathbb{F}_\ell)$, sampling of the characteristic polynomials of Frobenius, and the Khare--Wintenberger modularity theorem. The algorithm has been submitted for integration into Sage, executed on all of the genus~$2$ curves with trivial endomorphism ring in the LMFDB, and the results incorporated into the homepage of each such curve.

math.NT↗

arXiv2018

On a Modification of the Agrawal-Biswas Primality Test

We present a variant of the Agrawal-Biswas algorithm, a Monte Carlo algorithm which tests the primality of an integer $N$ by checking whether or not $(x+a)^N$ and $x^N + a$ are equivalent in a residue ring of $\mathbb{Z}/N\mathbb{Z}[x]$. The variant that we present is also a randomization of Lenstra jr. and Pomerance's improvement to the Agrawal-Kayal-Saxena deterministic primality test. We show that our variant of the Agrawal-Biswas algorithm can be used with the Miller-Rabin primality test to yield an algorithm which is slower than the Miller-Rabin test but relatively more accurate.

math.NT↗